Question: Solve for $a$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $60a+64 \geq 80a -92$
Solution: $\begin{aligned}60a+64 & \geq 80a -92 \\\\ 60a&\geq 80a-156 &(\text{Subtract } 64 \text{ from both sides}) \\\\ -20a &\geq -156 &(\text{Subtract } 80a \text{ from both sides})\\\\ 20a&\leq 156&(\text{Multiply both sides by }-1)\\\\ a&\leq\dfrac{39}{5}&(\text{Divide both sides by }20 \text{ and simplify}) \end{aligned}$ [Why did the inequality sign flip when we multiplied by -1?] In conclusion, the answer is $a \leq \dfrac{39}{5}$.